How to make flat spirals
You may do it using Spirals of the Curve Extra Objects add on.


Activate the add on in User Preferences-->Add-ons (Ctrl+Alt+U).


Add a spiral and play with its settings (Spirals panel in a Tool Shelf).



Extend the spiral's lenght extruding the curve's points. Add a Bezier Circle in the same position as the spiral is. Scale it to give a curve a desired thickness. Apply its transformations (Ctrl+A-->Rot&amp;Scale).


Select the spiral in Object Mode, go to the Curve Data header and set the Bezier Circle as a target of the beveled object.


Select the very top point of the curve, enable proportional editing and translate it along Z axis a bit to hide the ugly end of a curve.


You should get something like this:


To make make it gradually thinner in the inside select the very top point of the curve and scale it a bit with Alt+S using the proportional editing. Then scale it with S with a big proportional size falloff.


You may also use the proportional editing to easy change the curve's height.